A^TA + B?

Hong Zhang hzhang at mcs.anl.gov
Fri Oct 26 09:45:45 CDT 2007

> I would like to implement B = A^TA + B.
> And the transpose multiplication can be done with the following function,
> PetscErrorCode PETSCMAT_DLLEXPORT MatMatMultTranspose(Mat A,Mat B,MatReuse 
> scall,PetscReal fill,Mat *C) 
> since I would like to save some memory, I don't want to create an 
> intermediate matrix. In the above function, the discription of
> the argument "scall" is not clear, I know that MAT_INITIAL_MATRIX will create 
> a new empty matrix and the result will be stored.

> what about MAT_REUSE_MATRIX ?  does it mean that the C matrix will be added 
> with the result?

When the product matrix C=A^T*B is previously computed,
and you want repeating C=A^T*B, in which A and B maintain
the same non-zero 
sparse pattern but with different numerical values, using
MAT_REUSE_MATRIX will skip the symbolic computation of C=A^T*B
and reuse the exiting matrix data structure and memory of C.

Why do you need B = A^TA + B?
If your matrices are dense, you should use lapack or scalapack.
Sparse matrix product should be avoided because
the product matrix C usually is much denser than A and B,
and C=A^T*B cannot be implemented efficiently in general.
We provide MatMatMultTranspose() mainly for multigrid computation
in which the matrices have special data structure.



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